Greeks (Vanilla vs Binary Option)

Summary

Delta

Vanilla Option

  • Delta determines the rate of change of option price with respect to asset price/spot.
  • Delta ranges from 0 to 1 for CALL and -1 to 0 for PUT.
  • As the time remaining to expiration grows shorter, the time value of the option evaporates and correspondingly, the delta of in-the-money options increases while the delta of out-of-the-money options decreases.
  • As volatility rises, the time value of the option goes up and this causes the delta of out-of-the-money options to increase and the delta of in-the-money options to decrease.

Binary Option

  • Delta determines the rate of change of option price with respect to asset price/spot.
  • For a binary put, delta is a downward bell curve.
  • It’s evenly distributed between and achieved lowest delta for ATM option.
  • The shorter the time to maturity/IV, the lower sensitivity to change of price against spot.

Theta

Vanilla Option

  • Theta determines the rate of change of option price with respect to time.
  • Theta achieves its lowest point at ATM, and exponentially goes back to 0.
  • Theta is 0 for deep ITM/OTM contract.
  • The theta is highly sensitive around ATM; This is pretty obvious as such options have the highest time value and thus have more premium to lose each day.
  • The shorter the time to maturity, the higher sensitivity to change of price against time.
  • Options of high volatility stocks have higher theta than low volatility stocks.
  • This is because the time value premium on these options are higher and so they have more to lose per day.

Binary Option

  • Theta determines the rate of change of option price with respect to time.
  • Theta achieves its highest point at slightly ITM, lowest at slightly OTM.
  • Theta is 0 for ATM, indicating time to maturity does not affect ATM option price.
  • The theta is highly sensitive around ATM as the payout is deterministic around strike.
  • The shorter the time to maturity, the higher sensitivity to change of price against time.
  • The binary put options are having the fairly steady maximum absolute value of Vega irrespective of the IV; the decay is slightly lower for higher IV.

Vega

Vanilla Option

  • Vega determines the rate of change of option price with respect to implied volatility.
  • Vega achieves the its highest point at slightly OTM, lowest at slightly ITM.
  • The more time remaining to option expiration, the higher the vega.
  • This makes sense as time value makes up a larger proportion of the premium for longer term options and it is the time value that is sensitive to changes in volatility.

Binary Option

  • Vega determines the rate of change of option price with respect to implied volatility.
  • Vega achieves the its highest point at slightly OTM, lowest at slightly ITM. (reverse plot of Theta above)
  • Vega is 0 for ATM, indicating implied volatility does not affect ATM option price.
  • The vega is highly sensitive around ATM as the payout is deterministic around strike.
  • The binary put options are having the fairly steady maximum absolute value of Vega irrespective of the duration; the decay is slightly lower for higher duration.

Gamma

Vanilla Option

  • Gamma determines the rate of change of Delta with respect to spot; which can be explained easily by referring to Delta chart.
  • As the time to expiration draws nearer, the gamma of at-the-money options increases while the gamma of in-the-money and out-of-the-money options decreases.

Explanation of different volatility due to time value

  • When volatility is low, the gamma of at-the-money options is high while the gamma for deeply into or out-of-the-money options approaches 0.

  • This phenomenon arises because when volatility is low, the time value of such options are low, but it goes up dramatically as the underlying stock price approaches the strike price.

  • When volatility is high, gamma tends to be stable across all strike prices.

  • This is due to the fact that when volatility is high, the time value of deeply in/out-of-the-money options are already quite substantial.

  • Thus, the increase in the time value of these options as they go nearer the money will be less dramatic and hence the low and stable gamma.

Binary Option

  • Gamma determines the rate of change of Delta with respect to spot; which can be explained easily by referring to Delta chart.
  • Gamma charts has similiar pattern like Vega, but longer duration/higher IV turns out to be less sensitive towrards the change of spots.

Vanna

Vanilla Option

  • Vanna determines the rate of change of Delta with respect to volatility, or rate of change of Vega with respect to spot; can be explained with attached Vega chart.
  • Originally Vanna is useful to maintain a delta/vega hedged portfolio as an effectiveness checking.
  • Vanna achieves 0 at ATM, symmetrically highest at slightly ITM/OTM.
  • Shorter duration contracts/lower IV contracts will have a larger vanna chart due to high sensitvity of Delta towards price.

Binary Option

  • Vanna determines the rate of change of Delta with respect to volatility, or rate of change of Vega with respect to spot; can be explained with attached Vega chart.
  • Originally Vanna is useful to maintain a delta/vega hedged portfolio as an effectiveness checking.
  • Vanna achieves the its highest point at ATM, symmetrically lowest at slightly ITM/OTM.
  • Shorter duration contracts/lower IV contracts will have a larger vanna chart due to high sensitvity of Delta towards price.

Volga

Vanilla Option

  • Volga determines the rate of change of Vega with respect to volatility.
  • Useful to maintain a delta/vega hedged portfolio as an effectiveness checking.
  • Volga is 0 for ATM option; as Vega is 0 for ATM option.
  • Volga graph is assymetrical; observed a higher absolute magnitude of Volga for Put OTM and **Call ITM*option.

Binary Option

  • Volga determines the rate of change of Vega with respect to volatility, useful to maintain a delta/vega hedged portfolio as an effectiveness checking.
  • Volga is 0 for ATM option; as Vega is 0 for ATM option.
  • Volga graph is assymetrical; observed a higher absolute magnitude of Volga for OTM option.
  • The binary put options are having the fairly steady maximum absolute value of Vega irrespective of the duration; the decay is slightly lower for higher duration.